Complete/incomplete multi‐view subspace clustering via soft block‐diagonal‐induced regulariser

Abstract

Abstract This study proposes a novel multi‐view soft block diagonal representation framework for clustering complete and incomplete multi‐view data. First, given that the multi‐view self‐representation model offers better performance in exploring the intrinsic structure of multi‐view data, it can be nicely adopted to individually construct a graph for each view. Second, since an ideal block diagonal graph is beneficial for clustering, a ‘soft’ block diagonal affinity matrix is constructed by fusing multiple previous graphs. The soft diagonal block regulariser encourages a matrix to approximately have (not exactly) K diagonal blocks, where K is the number of clusters. This strategy adds robustness to noise and outliers. Third, to handle incomplete multi‐view data, multiple indicator matrices are utilised, which can mark the position of missing elements of each view. Finally, the alternative direction of multipliers algorithm is employed to optimise the proposed model, and the corresponding algorithm complexity and convergence are also analysed. Extensive experimental results on several real‐world datasets achieve the best performance among the state‐of‐the‐art complete and incomplete clustering methods, which proves the effectiveness of the proposed methods.

Keywords

• graph theory
• matrix algebra
• pattern clustering